Computation of excess stormflow at the basin scale
Prof. Pierluigi Claps
Dept. DIATI, Politecnico di Torino Pierluigi.claps@polito.it
losses
include:
•
interception, evapotranspiration, storage• infiltration, percolation
Interception, evapotranspiration, storage
First, the falling precipitation may be intercepted by the vegetation or depression storage in an area.
It is typically either distributed as runoff or evaporated back to the atmosphere.
The leafy matter may also be a form of interception.
Interception may be referred to as an abstraction and is accounted for as initial abstraction in some models.
Infiltration...
Precipitation reaching the ground may infiltrate.
This is the process of moving from the atmosphere into the soil.
Infiltration may be regarded as either a rate or a total. For example: the soil can infiltrate 1.2 inches/hour. Alternatively, we could say the soil has a total infiltration capacity of 3 inches.
Note that in both cases the units are Length or length per time!
Percolation...
The percolating water may move as a saturated front - under the
influence of gravity…
Once the water infiltrates into the ground, the downward movement of water through the soil profile may begin.
Or, it may move as unsaturated flow mostly due to capillary forces.
Some Runoff Production Models
• Phi-Index
• Psi-Index
• Bucket Model
• SCS Curve Number
Constant Infiltration Rate
A constant infiltration rate is the most simple of the
methods. It is often referred to as a phi-index or !-index.
In some modeling situations it is used in a conservative mode.
The saturated soil conductivity may be used for the infiltration rate.
The obvious weakness is the inability to model changes in infiltration rate.
The phi-index may also be estimated from individual storm events by looking at the runoff hydrograph.
Q=P-"#
Hydrograph Breakdown
0.0000 100.0000 200.0000 300.0000 400.0000 500.0000 600.0000 700.0000
0.000 0
0.160 0
0.320 0
0.480 0
0.640 0
0.800 0
0.960 0
1.120 0
1.280 0
1.440 0
1.600 0
1.760 0
1.920 0
2.080 0
2.240 0
2.400 0
2.560 0
2.720 0
2.880 0
3.040 0
3.200 0
3.360 0
3.520 0
3.680 0
Baseflow Surface
Response
Hydrograph Breakdown
0.0000 100.0000 200.0000 300.0000 400.0000 500.0000 600.0000 700.0000
0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000
Total Hydrograph
Surface Response
Baseflow
Derive phi-index
0 5000 10000 15000 20000 25000
0 8 16 24 32 40 48 56 64 72 80 88 96 104 112
120 128 Time (hrs.)
Flow (cfs)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Precipitation (inches)
Summing Flows -> Runoff Volume
Continuous process represented with discrete time steps
Estimating Excess Precip.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 1718 19
Time (hrs.)
Precipitation (inches)
Uniform loss rate of 0.2 inches per hour.
V = excess precipitation
V = runoff volume
Phi-Index Summary
• Phi-index computed as Q-P in volume.
• Uniform loss rate.
• If the precipitation stops for a time period, the infiltration will still be the same when the
precipitation starts again.
• Regardless of this weakness, this is still very powerful information to have regarding the response of a watershed.
$ index Method
• Used for medium-scale basins or catchments
• Estimates the peak discharge (q) from an area
– where $ is the runoff coefficient (proportional loss) – i is the rainfall intensity (mm/h)
– A is the drainage basin area (km2)
– F is a units conversion factor = 1/3.6 for [q]=m3/s
$has the meaning of the fraction of area that actively contributes to runoff
F A i
q = " ! ! !
Basic Conceptual Models
• Bucket model
– Most simple model – Fixed water capacity – No soil charaterictics – No vegetation
Precipitation Evaporation
Bucket capacity Water level in
bucket
Runoff
• The Biosphere
Atmosphere Transfer Scheme (BATS)
– Two soil layers
– One vegetation layer
Vegetation layer
Upper soil layer Root zone layer Total active layer Ground
Soil Layer 1 Soil Layer 2
Soil Layer Starts filling up with water Soil Layer Keeps Filling When the layer is full,
dump all the extra water into the next layer
Soil Layer Starts filling up with water Soil Layer Keeps Filling When the layer is full,
dump all the extra water into the next layer And So On…...
The BATS Model
• SiB (Simple Biosphere)
– Two vegetation layers – Three soil layers
Trees and shrubs
Upper thin soil layer Root zone layer Recharge layer Grass
Ground
• Bucket, BATS and SiB models are 1-D models (vertical)
• Ignore horizontal interactions between adjacent cells
• Used in 3-D atmospheric models
• Only three land components (soil, snow and vegetation)
• No vegetation types
• No runoff
• P = Precipitation
– Heavy precipitation causes more runoff than light precipitation
• S = Storage Capacity
– Soils with high storage produce less runoff than soils with little storage capacity.
• F = Current Storage
– Dry soils produce less runoff than wet soils
Conceptual Equivalent of the
SCS-CN Model
SCS method
• Soil conservation service (SCS) method is an
experimentally derived method to determine rainfall excess using information about soils, vegetative cover, hydrologic condition and antecedent moisture conditions
• The method is based on the simple relationship:
Pe = P - Fa – Ia
Pe is runoff volume, P is precipitation volume, Fa is continuing abstraction, and Ia is the sum of initial losses
(depression storage, interception, ET)
Time
Precipitation
tp
Ia Fa
Pe
a a
e I F
P P= + +
Abstractions – SCS Method
• In general
• After runoff begins
• Potential runoff
• SCS Assumption
• Combining SCS assumption with P=Pe+Ia+Fa
Time
Precipitation
tp
Ia Fa
Pe
a a
e I F
P P= + +
Storage Maximum Potential
S
n Abstractio Continuing
n Abstractio Initial
Excess Rainfall
Rainfall Total
=
=
=
=
=
a a e
F I P P
P Pe !
S Fa !
Ia
P !
a e a
I P
P S
F
= !
( )
S I P
I P P
a e a
+
!
= !
2
SCS Method (Cont.)
• Experiments showed
• So
S Ia =0.2
( )
S P
S Pe P
8 . 0
2 .
0 2
+
= !
0 1 2 3 4 5 6 7 8 9 10 11 12
0 1 2 3 4 5 6 7 8 9 10 11 12
Cumulative Rainfall, P, in
Cumulative Direct Runoff, Pe, in
100 90 80 70 60 40 20 10
• Surface
– Impervious: CN = 100 – Natural: CN < 100
100) CN
0 Units;
American (
1000 10
<
<
!
= CN S
S =25400 CN ! 254 (SI Units;0 < CN < 100)
SCS Method (Cont.)
• SCS Curve Numbers depend on soil conditions!..
Group Minimum Infiltration
Rate (in/hr) Soil type
A 0.3 – 0.45 High infiltration rates. Deep, well drained sands and gravels
B 0.15 – 0.30 Moderate infiltration rates. Moderately deep, moderately well drained soils with moderately coarse textures (silt, silt loam) C 0.05 – 0.15 Slow infiltration rates. Soils with layers, or
soils with moderately fine textures (clay loams)
D 0.00 – 0.05 Very slow infiltration rates. Clayey soils, high water table, or shallow impervious layer
Soil Initial Conditions
5-day antecedent rainfall, inches Antecedent moisture
Dormant Season Growing Season
I Less than 0.5 Less than 1.4
II 0.5 to 1.1 1.4 to 2.1
III Over 1.1 Over 2.1
• Normal conditions, AMC(II)
• Dry conditions, AMC(I)
• Wet conditions, AMC(III) 10 0.058 ( )
) ( 2 . ) 4
( CN II
II I CN
CN = !
) ( 13 . 0 10
) ( ) 23
( CN II
II III CN
CN = +
!!on antecedent rainfall conditions
!and on land use, treatment and hydrologic
conditions!
- modeled in order to account for the destiny of the precipitation that falls and to evaluate the precipitation excess that causes the runoff
hydrograph.
The fate of the falling precipitation is:
